When manufacturing elastic twisted yarns with hollow spindles, as they are known, for example, from the DE 29 19 100 C2, DE 196 26 549 A1 or CH 200 628, the troublefree processing of the yarn is important for the economic efficiency and the quality of the finished product. Critical in these processes is the running behaviour of the elastic core yarn, for example Elastan. In particular when using fine core yarns (44 dtex, 22 dtex, 11 dtex or even finer yet), utilizing Elastan, and there most of all at low drafts (less than 3 times), breakdowns of many different types occur because of the low yarn tensions, which breakdowns can result in breakage of the yarn. The yarn tension of the core yarn from the point of removal from the feed bobbin to the point at which it is twisted above the exit from the hollow spindle is therefore a very important parameter. The behaviour of the core yarn in the thread channel of the hollow spindle has a decisive influence on the yarn tension. As a rule one must assume that the core yarn rests on the inner surface of the thread channel and rotates together with the hollow spindle. Until now the thread channel in the hollow spindle is created by means of a long bore. Thus the surface of the thread channel is cylindrical. A cylindrical surface contacts the core yarn along a contact line, which in particular due to the characteristics of the elastic core yarn results in a large amount of friction. This friction reduces the tension in the core yarn, which it has prior to entering the hollow spindle, which can lead to the abovedisclosed breakdowns. In the case of many types of yarns, in particular Elastan, an adhering effect also occurs between the yarn and the smooth surfaces of the thread channel, which can clearly further increase the friction force.